Problem:
In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by , , , , and . Find .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since appears in the first row, first column, and on diagonal, the sum of the remaining two numbers in each of these lines must be the same. Thus,
so and . now , and form a diagonal with a sum of , so we can find , and . Hence .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions